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Abstract:
We present a new, computationally efficient, energy-integrated approximation for neutrino effects in hot and dense astrophysical environments such as supernova cores and compact binary mergers and their remnants. Our new method, termed ileas for Improved Leakage-Equilibration-Absorption Scheme, improves the lepton number and energy losses of traditional leakage descriptions by a novel prescription of the diffusion time-scale based on a detailed energy integral of the flux-limited diffusion equation. The leakage module is supplemented by a neutrino-equilibration treatment that ensures the proper evolution of the total lepton number and medium plus neutrino energies as well as neutrino-pressure effects in the neutrino-trapping domain. Moreover, we employ a simple and straightforwardly applicable ray-tracing algorithm for including re-absorption of escaping neutrinos especially in the decoupling layer and during the transition to semitransparent conditions. ileas is implemented on a three-dimensional (3D) Cartesian grid with a minimum of free and potentially case-dependent parameters and exploits the basic physics constraints that should be fulfilled in the neutrino-opaque and free-streaming limits. We discuss a suite of tests for stationary and time-dependent proto-neutron star models and post-merger black hole–torus configurations, for which 3D ileas results are demonstrated to agree with energy-dependent 1D and 2D two-moment (M1) neutrino transport on the level of 10–15 per cent in basic neutrino properties. This also holds for the radial profiles of the neutrino luminosities and the electron fraction. Even neutrino absorption maps around torus-like neutrino sources are qualitatively similar without any fine-tuning, confirming that ileas can satisfactorily reproduce local losses and re-absorption of neutrinos as found in sophisticated transport calculations.
